Fraction Calculator — Add, Subtract, Multiply, and Divide Fractions — FreeTool24

Fraction calculator — math calculations

Fractions are everywhere: halving a recipe, splitting a bill, calculating percentages, or reading a ruler. Yet fraction arithmetic trips up more people than almost any other basic math topic. The rules for adding and dividing fractions are genuinely different from whole-number arithmetic, and the steps are easy to forget if you learned them years ago.

This guide walks through every operation — adding, subtracting, multiplying, and dividing fractions — with full step-by-step examples. The Fraction Calculator handles the computation automatically and shows every working step so you can learn alongside it.

What is a fraction?

A fraction represents a part of a whole. It has two components:

  3   ← numerator (how many parts you have)
 ─── 
  4   ← denominator (total equal parts the whole is divided into)

So 3/4 means "3 out of 4 equal parts."

Types of fractions

Type	Example	Description
Proper fraction	3/4	Numerator < denominator
Improper fraction	7/4	Numerator ≥ denominator
Mixed number	1 3/4	Whole number + proper fraction
Equivalent fractions	1/2 = 2/4 = 3/6	Same value, different form
Unit fraction	1/5	Numerator is always 1

How to simplify a fraction

Simplifying (reducing) a fraction means dividing both the numerator and denominator by their greatest common divisor (GCD) until no common factor remains other than 1.

Example: Simplify 18/24

Find the GCD of 18 and 24
- Factors of 18: 1, 2, 3, 6, 9, 18
- Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
- GCD = 6
Divide both by 6: 18 ÷ 6 = 3, 24 ÷ 6 = 4
Result: 3/4 ✓

Quick tip: If you cannot find the GCD, keep dividing by small primes (2, 3, 5, 7) until the fraction will not reduce further.

How to add fractions

Same denominator

When the denominators are the same, just add the numerators:

1   2   1 + 2   3
─ + ─ = ───── = ─
5   5     5     5

Different denominators

When denominators differ, you must find the least common denominator (LCD) first.

Example: 1/3 + 1/4

Step 1: Find the LCD of 3 and 4

Multiples of 3: 3, 6, 12, 15…
Multiples of 4: 4, 8, 12, 16…
LCD = 12

Step 2: Convert each fraction to the LCD

1   1 × 4   4
─ = ───── = ──
3   3 × 4   12

1   1 × 3   3
─ = ───── = ──
4   4 × 3   12

Step 3: Add the numerators

4    3    7
── + ── = ──
12   12   12

Step 4: Simplify if possible — 7/12 is already in lowest terms.

Result: 7/12

How to subtract fractions

Subtraction follows the same process as addition — find the LCD, convert, then subtract the numerators.

Example: 5/6 − 1/4

Step 1: LCD of 6 and 4

Multiples of 6: 6, 12, 18…
Multiples of 4: 4, 8, 12, 16…
LCD = 12

Step 2: Convert

5   5 × 2   10
─ = ───── = ──
6   6 × 2   12

1   1 × 3   3
─ = ───── = ──
4   4 × 3   12

Step 3: Subtract

10    3    7
── − ── = ──
12   12   12

Result: 7/12

How to multiply fractions

Multiplication is the easiest fraction operation — multiply straight across.

a   c   a × c
─ × ─ = ─────
b   d   b × d

Example: 2/3 × 3/5

2 × 3   6   2
───── = ─ = ─
3 × 5   15  5

Shortcut — cross-cancel before multiplying: If any numerator shares a factor with any denominator, cancel first to keep numbers small.

2/3 × 3/5: the 3 in the numerator and 3 in the first denominator cancel → (2/1) × (1/5) = 2/5

Result: 2/5

How to divide fractions

To divide by a fraction, multiply by its reciprocal (flip the second fraction, then multiply).

a   c   a   d   a × d
─ ÷ ─ = ─ × ─ = ─────
b   d   b   c   b × c

Example: 3/4 ÷ 2/5

Step 1: Flip the second fraction: 2/5 → 5/2

Step 2: Multiply

3   5   15
─ × ─ = ──
4   2    8

Step 3: Convert to mixed number if needed: 15/8 = 1 7/8

Result: 1 7/8

Memory trick: "Keep, Change, Flip" — Keep the first fraction, Change ÷ to ×, Flip the second fraction.

How to work with mixed numbers

A mixed number like 2 3/4 means 2 + 3/4. To use a mixed number in any calculation, first convert it to an improper fraction.

Converting mixed number → improper fraction

Multiply the whole number by the denominator, then add the numerator.

2 3/4 → (2 × 4) + 3 = 11 → 11/4

Converting improper fraction → mixed number

Divide numerator by denominator.
Quotient = whole number, Remainder = new numerator.

11/4 → 11 ÷ 4 = 2 remainder 3 → 2 3/4

Example: 1 1/2 + 2 2/3

Convert: 1 1/2 = 3/2, 2 2/3 = 8/3
LCD of 2 and 3 = 6
Convert: 3/2 = 9/6, 8/3 = 16/6
Add: 9/6 + 16/6 = 25/6
Simplify: 25/6 = 4 1/6

Result: 4 1/6

Common mistakes with fractions

❌ Adding denominators

Wrong:  1/3 + 1/4 = 2/7
Right:  1/3 + 1/4 = 7/12

Never add or subtract the denominators. Find the LCD and add only the numerators.

❌ Forgetting to find the LCD

Wrong:  2/3 + 1/6 = 3/9 = 1/3
Right:  2/3 + 1/6 = 4/6 + 1/6 = 5/6

❌ Flipping the wrong fraction when dividing

Wrong:  3/4 ÷ 2/5 = 3/4 × 4/2
Right:  3/4 ÷ 2/5 = 3/4 × 5/2  ← flip the SECOND fraction

❌ Not simplifying the final answer

Always check whether your result can be reduced. If numerator and denominator share any common factor, divide both by it.

Fraction rules — quick reference

Operation	Rule	Example
Add (same denom.)	Add numerators	2/7 + 3/7 = 5/7
Add (diff. denom.)	Find LCD, then add	1/2 + 1/3 = 3/6 + 2/6 = 5/6
Subtract	Same as add, subtract numerators	5/6 − 1/4 = 10/12 − 3/12 = 7/12
Multiply	Multiply across	2/3 × 3/4 = 6/12 = 1/2
Divide	Multiply by reciprocal	2/3 ÷ 3/4 = 2/3 × 4/3 = 8/9
Simplify	Divide by GCD	6/8 ÷ 2/2 = 3/4

Real-world fraction examples

Cooking: scaling a recipe

A recipe calls for 3/4 cup of flour and you want to make 1.5× the batch.

3/4 × 3/2 = 9/8 = 1 1/8 cups

Carpentry: cutting wood

You have a 7/8 inch board and need to cut 3/8 inches off it.

7/8 − 3/8 = 4/8 = 1/2 inch remaining

Finance: splitting a bill

A $85 bill is split between 3 people but person A pays double.

Total shares: 1 + 1 + 2 = 4
Person A pays 2/4 = 1/2 of $85 = $42.50

Time: estimating tasks

A task takes 2/3 of an hour. How long for 5 tasks?

2/3 × 5 = 10/3 = 3 1/3 hours

How to find the least common denominator (LCD)

The LCD is the smallest number divisible by both denominators. There are two reliable methods:

Method 1: List multiples

List multiples of each denominator until you find one in common.

LCD of 4 and 6:
Multiples of 4: 4, 8, 12, 16…
Multiples of 6: 6, 12, 18…
LCD = 12

Method 2: Prime factorization

Factor each denominator, then take the highest power of each prime factor.

LCD of 12 and 18:
12 = 2² × 3
18 = 2 × 3²
LCD = 2² × 3² = 4 × 9 = 36

Frequently asked questions

How do I add three or more fractions? Find the LCD of all denominators at once, convert every fraction to that denominator, then add all numerators. Example: 1/2 + 1/3 + 1/4 → LCD = 12 → 6/12 + 4/12 + 3/12 = 13/12 = 1 1/12.

What is an equivalent fraction? Two fractions are equivalent if they represent the same value. Multiply or divide both numerator and denominator by the same number: 1/2 = 2/4 = 3/6 = 50/100. To check if two fractions are equivalent, cross-multiply: a/b = c/d if a × d = b × c.

How do I convert a decimal to a fraction? Write the decimal over its place value. 0.75 = 75/100 = 3/4. For repeating decimals, let x = 0.333…, then 10x = 3.333…, so 9x = 3, x = 1/3.

How do I compare two fractions? Cross-multiply. For a/b vs c/d: compare a × d with b × c. The fraction with the larger product is bigger. Or convert both to the LCD and compare numerators.

What is a complex fraction? A fraction where the numerator, denominator, or both are themselves fractions. Example: (1/2)/(3/4). Simplify by multiplying the outer fraction by the reciprocal of the denominator: (1/2) × (4/3) = 4/6 = 2/3.

Why do we need fractions when we have decimals? Fractions are exact — 1/3 cannot be expressed as a finite decimal (0.3333… repeats forever). In cooking, woodworking, and many engineering applications, fractional measurements are more precise and easier to work with than their decimal approximations.

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